WASHINGTON — A woman with a 1-year-old child in her car was fatally shot by police near the US Capitol on Thursday, after a chase through the heart of Washington that brought a new jolt of fear to a city already rattled by the recent Navy Yard shooting and the federal shutdown.

The car was registered to Miriam Carey, 34, a dental hygienist from Stamford, Conn., law enforcement officials said, adding that they believed Carey was the driver.

District of Columbia Police Chief Cathy Lanier said the driver tried to breach two landmarks and that the incident was not an accident. But officials also said it did not appear to part of any larger or organized terrorist plot.

The chase began about 2:15 p.m. at a White House security checkpoint, where the black Infiniti driven by the woman struck a barrier and a Secret Service officer. The woman drove away and headed to the Capitol.

During the chase, police officers opened fire twice, both times in areas busy with tourists and office workers. The Capitol itself was locked down, as a debate over the government shutdown was interrupted by echoes of shots, officers with guns, and an urgent order to ‘‘shelter in place.’’

The end came outside the Hart Senate Office Building, at Maryland Avenue and Second Street NE. The woman’s car got stuck. Officers fired another volley. Then, moments later, an officer emerged with the child, carrying the toddler away as new waves of officers arrived.

Authorities said the woman was not armed, and although the incident was first reported as a shooting at the Capitol, the only shots were fired by officers.

Police said there was no indication that the woman was part a larger threat. But they said little about why she had suddenly become a threat herself.

‘‘I am pretty confident this was not an accident,’’ Lanier said at a news conference.

Lanier said that the child was in good condition and in protective custody. Two officers were injured in the chase along Pennsylvania Avenue, but neither was seriously hurt.

The chaotic day caught Washington at an unusually low moment. Just days after the government shut down because of a budget impasse and weeks after 12 people were killed at the nearby Navy Yard, the notion of gunfire and a car hurtling from the White House to the Capitol had the city thinking the worst.

It began with something not that unusual — a driver with out-of-state plates turning into a blocked entry near the White House.

It quickly became something else.

‘‘Whoa! Whoa!,’’ Secret Service officers were shouting at the car, according to a witness, Shawn Joseph, 29. ‘‘It looked liked [the driver was] scared or lost. I thought they might have been a tourist.’’

But then, witnesses said, officers tried to place a barrier in front of the car. The driver swerved. The officers moved the barrier. She hit it, and a Secret Service officer was thrown up on the hood and then off the car.

The officer was not badly hurt. The driver fled east and was stopped by police at a small traffic circle at the foot of Capitol Hill. There, video shot by the US-funded Arabic TV station Alhurra shows officers with guns pointed at the car. The driver took off.

‘‘I thought it was a motorcade,’’ Ryan Christiansen of Idaho Falls, Idaho, said when he saw the black car trailed by police cars with sirens wailing. Then, Christiansen said, the car ‘‘was pulling away, and somewhere between six and eight shots were fired,’’ he said.

Despite the shots, the driver continued. She went around another traffic circle and then up Constitution Avenue toward the peak of Capitol Hill.

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